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### Question 1

An electronics shop sold 24 TV sets at a 2% profit, and 4 Coolers at 23% profit. What is the average percentage profit earned by the shop?

**A**

5%.

**B**

6%.

**C**

4%.

**D**

8%.

**Soln.**

**Ans: a**

We shall use the alligation formula. If a sample n_{1} has an average property of A_{1}, and another sample n_{2} has an average property of A_{2}, then the average property of the mixture, A, is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting A_{2} = 23, A_{1} = 2, n1 = 24, n2 = 4, we have 24 × (A - 2) = 4 × (23 - A), from where we get A = 5%. *The "property" in the alligation formula could be percentage, speed, weight, price, etc.,*

### Question 2

A 300 liter mixture of milk and water contains 62% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

**A**

72 liter.

**B**

73 liter.

**C**

71 liter.

**D**

75 liter.

**Soln.**

**Ans: a**

The volume of milk will remain same at ${62 × 300}/100$ = 186 liters. The amount of water at present is 300 - 186 = 114 liters. We need to make the volume of water equal to that of the milk. So we have to add 186 - 114 = 72 liters of water.

### Question 3

A milkman has 16 liters of 11% curd, and 4 liters of 21% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

### Question 4

21 Kg of Grade I sugar costing Rs. 24/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 4/Kg. What is the price of the mixture per Kg?

**A**

Rs. 18 per Kg.

**B**

Rs. 19 per Kg.

**C**

Rs. 17 per Kg.

**D**

Rs. 21 per Kg.

**Soln.**

**Ans: a**

We shall use the alligation formula. If a sample n_{1} has an average price of A_{1}, and another sample n_{2} has an average price of A_{2}, then the price of the mixture, A, is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting A_{2} = 4, A_{1} = 24, n1 = 21, n2 = 9, we have 21 × (A - 24) = 9 × (4 - A), from where we get A = Rs. 18 per Kg.

### Question 5

A mixture of milk and water contains 5 parts of milk and 1 parts of water. How much fraction of the mixture should be removed and replaced by water so that ratio of water and milk becomes equal?

**A**

${2/5}$.

**B**

$1{3/4}$.

**C**

$1{5/7}$.

**D**

$2{3/7}$.

**Soln.**

**Ans: a**

Let the volume of the mixture be 5 + 1 = 6 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $1 - {1x}/6 + x$. The volume of the milk in the new mixture would be $5 - {5x}/6.$ Equating the two volumes and solving for x we get x = ${6 × 4}/{2 × 5}$. The fraction that must be removed = $1/6$ × ${6 × 4}/{2 × 5}$, which gives $4/{2 × 5}$ = ${2/5}$.

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This Blog Post/Article "Alligations and Mixtures Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-07